This sample size calculator tells you how many responses a survey needs for a target margin of error at a given confidence level.
Statistics
Sample Size Calculator
Estimate sample size from confidence level, margin and proportion.
Calculator
About this calculator
Formula notes
n = z²·p(1−p) / e². With p = 0.5 for the conservative maximum.
Worked examples
- Example: 95% confidence and ±5% margin gives n = 1.96²·0.25 / 0.0025 ≈ 385 respondents.
- At 95% confidence, 5% margin, and expected proportion 50%, the large-population estimate is about 385 completed responses.
How to use it
- Choose the confidence level.
- Set the margin of error you can tolerate.
- Read the minimum sample size, rounding up.
Frequently asked questions
Why is the classic answer 385?
1.96² × 0.25 / 0.05² = 384.16, which rounds up to 385.
What if I expect a skewed proportion?
Replace p = 0.5 with your expected value; n will drop because p(1−p) shrinks.
Limits and interpretation
- The calculation assumes a probability sample and addresses sampling precision, not response rate, design effects, clustering, or bias.
- Required invitations usually exceed completed sample size, and subgroup analysis may require larger targets.